Question

Gabriel is raising money for a school trip by selling lollipops and bags of chips. The price of each lollipop is $1 and the price of each bag of chips is $1.50. Yesterday Gabriel made $30 from selling a total of 26 lollipops and bags of chips. Graphically solve a system of equations in order to determine the number of lollipops sold, x,x, and the number of bags of chips sold, yy.

Answer 1

`x + (3)/(2) y = 30`

and

`x + y = 26`

Answer 2

• 18 lollipops
• 8 bags of chips

Explanation:

The equations we want to graph are one for the revenue, and one for the number of items sold.

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revenue

The revenue from each lollipop is $1, so the revenue in dollars from selling x of them is 1·x = x. The revenue from each bag of chips is $1.50, so the revenue from selling y of them is 1.50·y = 1.5y. The total revenue from selling x lollipops and y bags of chips is ...

x +1.5y = 30 . . . . . dollars

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item count

The total number of items sold is ...

x + y = 26

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solution

The graph shows the solution to these two equations is ...

(x, y) = (18, 8)

The number of lollipops sold is 18; the number of bags of chips sold is 8.